Maximally fast coarsening algorithms

We present maximally-fast numerical algorithms for conserved coarsening systems that are stable and accurate with a growing natural time-step $\Delta t=At_s^{2/3}$. We compare the scaling structure obtained from our maximally-fast conserved systems directly against the standard fixed-timestep Euler algorithm, and find that the error scales as $\sqrt{A}$ --- so arbitrary accuracy can be achieved. For non-conserved systems, only effectively finite timesteps are accessible for similar unconditionally stable algorithms.